论文标题
3D中各向异性库仑能量的显式极小剂
Explicit minimisers for anisotropic Coulomb energies in 3D
论文作者
论文摘要
在本文中，我们考虑了三个维度的一般各向异性能量，并给出了它们的最小化剂的完整表征。我们表明，根据相互作用势的傅立叶变换，最小化器要么是椭圆形的归一化特征函数，要么是在二维椭圆上支持的度量。特别是，如果转换严格为正，则始终是一个椭圆形，而当傅立叶变换归化时，两种情况都可能发生。最后，我们显示了一个明确的示例，其中确实发生了最小化的维度损失。
In this paper we consider a general class of anisotropic energies in three dimensions and give a complete characterisation of their minimisers. We show that, depending on the Fourier transform of the interaction potential, the minimiser is either the normalised characteristic function of an ellipsoid or a measure supported on a two-dimensional ellipse. In particular, it is always an ellipsoid if the transform is strictly positive, while when the Fourier transform is degenerate both cases can occur. Finally, we show an explicit example where loss of dimensionality of the minimiser does occur.
